(problem 13). margo's marginal utility of one dance lesson is 100 utils per lesson. her marginal utility of a new pair of dance shoes is 300 utils per pair. the price of a dance lesson is $50 per lesson. she currently spends all her income, and she buys her optimal consumption bundle. what is the price of a pair of dance shoes?

Since Margo purchase her optimal consumption bundle, the marginal utility per dollar consumed on dance lessons must be equivalent to the marginal utility per dollar paid on dance shoes. The marginal utility per dollar spent on dance lessons is 100 utils per lesson, where $50 per lesson is equivalent to 2 utils per dollar. The marginal utility per dollar expended on dance shoes therefore has to equal 2 utils per dollar. Since the marginal utility of a pair of dance shoes cost 300 utils per pair, the value of a pair of shoes should be $150 per pair, so that 300 utils per pair/$150 per pair is equal to: 2 utils per dollar.

a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.